In a skillet or sauté pan, melt butter over medium heat. Cook butter, turning occasionally, for 20 to 25 minutes, or until it turns dark brown. Take the butter off the heat. Lemon juice and vinegar are whisked in.
Place a large cast iron skillet over medium-high heat and add the oil. Put a piece of parsley in the skillet to check the temperature. Crisping indicates readiness.
Milk and eggs should be whisked in a shallow dish, and flour should be placed in a separate shallow dish. Add salt, pepper, and creole seasoning to fish before serving. Working with a single fillet at a time, coat the fish in flour, shake off the excess, and then coat it in the egg mixture. Filets are put back in the flour and then placed on a rack over a baking sheet.
Fry the fish in two batches for 5 to 6 minutes per side, or until golden brown. Remove, then dry off with paper towels.
Divide the fish among the four plates, then spread the sauce over it. Lemon slices and parsley are used as garnish.